Energy quantization for matter orbiting black hole and Hawking radiation

Abstract

The energy of a test particle orbiting a Schwarzschild black hole is quantized owing to the quantization of the angular momentum. For smallest stable circular orbit, the excitation energy is found to resemble closely the expression for the temperature of the Hawking radiation. This result is consistent with the Unruh effect for orbiting test particle. The predicted energy quantization might be observable by studies of the red-shifted 21-cm line of neutral hydrogen orbiting a primordial black hole with mass of the order of that of Earth.